(DP 线性DP 递推) leetcode 64. Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

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是leetcode62 的拓展题。

这个题就是求所经过的路中的数的总和的最小值。和leetcode62的代码是相差不大的，只是自重一些地方修改了。

C++代码：

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size(),n = grid[0].size();
        vector<vector<int> > dp(m,vector<int>(n,0));
        dp[0][0] = grid[0][0];
        for(int i = 1; i < m; i++){
            dp[i][0] = dp[i-1][0] + grid[i][0];  //要注意
        } 
        for(int j = 1; j < n; j++){
            dp[0][j] = dp[0][j-1] + grid[0][j]; //要注意
        }
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = grid[i][j] + min(dp[i-1][j],dp[i][j-1]);  //要注意
            }
        }
        return dp[m-1][n-1];
    }
};